@gregw BTR/score (or BTR/approval) is an excellent system, although it is not stable ex ante under majority preference—only a maximal lottery is. Maximal lotteries also satisfy participation and Condorcet (they can do that because they are inherently non-deterministic in the case of Condorcet cycles—those properties are incompatible for deterministic methods).

BTR was invented by Nicolaus Tideman. He is still around, I don’t know how accessible he is but he is certainly involved in voting theory. Sorting/tie-breaking by score or approval in BTR is an obvious extension.

For primaries, a specified multi-winner method is needed, which could be a “natural” extension of a single-winner method. Like peeling winners of BTR off recursively, although it may be more stable to prioritize candidates in the Smith/bipartisan set (those can lead to different results). A PR/multi-winner method would probably be theoretically preferable, maybe some others more versed in multi-winner methods can comment on options for simplicity.

Something on my mind, for any Condorcet method, even a maximal lottery, being intrinsically stable under majority preference after a winner is chosen is simply impossible with Condorcet cycles. My thinking lately is that there needs to be an external mechanism that compensates dissatisfied majorities in the event of a Condorcet cycle, but I don’t know what that mechanism ought to be or how it ought to be enforced.

Food for thought. I’m glad your reform efforts are picking up steam!